The Legislature on Tuesday overrode Gov. Paul LePage’s veto of a bill that diverts state funds to help Medicaid recipients give up smoking.

The governor vetoed the bill Jan. 10, saying the proposal eliminated a cost-sharing component that made Medicaid recipients pay for a portion of tobacco cessation programs. LePage, in his veto message, said removing the cost-sharing, or co-pay, expands “welfare unchecked and does nothing to move us in the direction of a sound fiscal house.”

“I am supportive of MaineCare (Medicaid) members taking steps to stop smoking,” LePage wrote. “However, I believe that cost sharing is an essential component of maintaining fiscal responsibility in our welfare programs as well as improving the success rate of our welfare programs generally.”

Proponents of the bill said it removes barriers for recipients of Medicaid, known as MaineCare here, who want to quit smoking and using tobacco. The bill passed the Senate without a roll call vote and the House, 140-1, last year.

The House voted 131-10 last week to override LePage’s veto. On Tuesday, the Senate completed the override with a 31-4 vote. Tuesday’s action was just one of about a half-dozen overrides of LePage vetoes since 2013.

“Unless you are making your money off Marlboros, I don’t know why anyone would be against helping people quit smoking,” said Senate Majority Leader Troy Jackson, D-Allagash, in a prepared statement. “Tobacco-related illnesses hurt our state and hurt our families. We should be doing everything we can to help people quit smoking, including passing this bill.”

L.D. 386 was sponsored by Rep. Linda Sanborn, D-Gorham. Sanborn said last week that the bill made scientific and fiscal sense. She cited a report by the Behavioral Risk Factor Surveillance System, which found that 42 percent of MaineCare members are smokers and 67 percent of those smokers report wanting to quit.

The bill directs the Department of Health and Human Services to draw money from the Fund for a Healthy Maine to pay for the initiative. According to the fiscal note adopted last year, the Fund for a Healthy Maine would direct $414,000 toward smoking cessation, while drawing nearly $670,000 in federal match money.

“By opening up access to treatment of tobacco addiction, we can save taxpayer money and lives,” said Sanborn.